Algebra Seminar

"The Category of Complexes, Part II"

Abstract:
We will begin this talk by defining the tensor product of (1) graded
R-modules and (2) their morphisms, and will see that these constructions
induce a functor from GM(R) x GM(R) into GM(R). Viewing a complex as a
graded R-module together with a differential, we will then be equipped
to define the tensor product of complexes of R-modules. These tensors
will then help to induce a functor from DGM(R) x DGM(R) into DGM(R),
which will commute with the aforementioned forgetful functor. Several
canonical isomorphisms, including the transposition of the tensor
product of two complexes, and an expression for the shift automorphism,
will be mentioned. Time permitting, we will proceedto investigate
homomorphisms of complexes.